Determining Functions from Ordered Pairs

The video tutorial explores the concept of functions in mathematics, focusing on whether a given relationship between X and Y is a function. It begins with an introduction to the topic, followed by an explanation of a table showing the relationship between X and Y. An interactive exercise is provided for viewers to determine if the relationship is a function after adding an ordered pair. The video defines a function as a relation where each input has a unique output and analyzes the table to conclude that the relationship is not a function due to repeated inputs with different outputs. The lesson concludes with a summary and encourages viewers to continue learning.

What is the main topic discussed in the video?

• Graphing linear equations

• Solving algebraic equations

• Determining if a relationship is a function

• The history of mathematics

What is the task given to the viewer regarding the table?

• To calculate the slope of the line

• To determine if the relationship is a function after adding an ordered pair

• To solve for X

• To find the maximum value of Y

What are viewers instructed to do after the task is explained?

• Skip to the end of the video

• Read a textbook

• Pause the video and attempt the task

• Watch another video

How is a function defined in the video?

• A relation where each input has multiple outputs

• A relation where each input has exactly one unique output

• A relation with no outputs

• A relation with only one input

What should each input in a function have?

• Multiple outputs

• Exactly one unique output

• No outputs

• At least two outputs

What happens to the table when the ordered pair (2, 2) is added?

• It remains unchanged

• It no longer represents a function

• It becomes a linear equation

• It becomes a function

Why does the table not represent a function after adding (2, 2)?

• Because X has multiple unique outputs

• Because X has a repeated input with different outputs

• Because Y has multiple inputs

• Because Y is not defined

What is the unique output for the input 2 before adding the new pair?

• 10

• 12

• 22

• 2

What is the ordered pair added to the table?

• (2, 2)

• (2, 12)

• (1, 2)

• (12, 2)

What is the relationship between X and Y before adding the new pair?

• X has multiple outputs

• Y is undefined

• X has a unique output

• Y has multiple inputs